Probability distributions of smeared quantum stress tensors

We obtain in closed form the probability distribution for individual measurements of the stress-energy tensor of two-dimensional conformal field theory in the vacuum state, smeared in time against a Gaussian test function. The result is a shifted Gamma distribution with the shift given by the previously known optimal quantum inequality bound. For small values of the central charge it is overwhelmingly likely that individual measurements of the sampled energy density in the vacuum give negative results. For the case of a single massless scalar field, the probability of finding a negative value is 84%. We also report on computations for four-dimensional massless scalar fields showing that the probability distribution of the smeared square field is also a shifted Gamma distribution, but that the distribution of the energy density is not.Comment: 9 pages, 1 figure. Minor edits implemente

Local Thermal Equilibrium in Quantum Field Theory on Flat and Curved Spacetimes

The existence of local thermal equilibrium (LTE) states for quantum field theory in the sense of Buchholz, Ojima and Roos is discussed in a model-independent setting. It is shown that for spaces of finitely many independent thermal observables there always exist states which are in LTE in any compact region of Minkowski spacetime. Furthermore, LTE states in curved spacetime are discussed and it is observed that the original definition of LTE on curved backgrounds given by Buchholz and Schlemmer needs to be modified. Under an assumption related to certain unboundedness properties of the pointlike thermal observables, existence of states which are in LTE at a given point in curved spacetime is established. The assumption is discussed for the sets of thermal observables for the free scalar field considered by Schlemmer and Verch.Comment: 16 pages, some minor changes and clarifications; section 4 has been shortened as some unnecessary constructions have been remove

The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes

Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.Comment: 21 pages, AMS-LaTeX, 2 figures appended as Postscript file

A Bisognano-Wichmann-like Theorem in a Certain Case of a Non Bifurcate Event Horizon related to an Extreme Reissner-Nordstr\"om Black Hole

Thermal Wightman functions of a massless scalar field are studied within the framework of a ``near horizon'' static background model of an extremal R-N black hole. This model is built up by using global Carter-like coordinates over an infinite set of Bertotti-Robinson submanifolds glued together. The analytical extendibility beyond the horizon is imposed as constraints on (thermal) Wightman's functions defined on a Bertotti-Robinson sub manifold. It turns out that only the Bertotti-Robinson vacuum state, i.e. $T=0$, satisfies the above requirement. Furthermore the extension of this state onto the whole manifold is proved to coincide exactly with the vacuum state in the global Carter-like coordinates. Hence a theorem similar to Bisognano-Wichmann theorem for the Minkowski space-time in terms of Wightman functions holds with vanishing ``Unruh-Rindler temperature''. Furtermore, the Carter-like vacuum restricted to a Bertotti-Robinson region, resulting a pure state there, has vanishing entropy despite of the presence of event horizons. Some comments on the real extreme R-N black hole are given

Breeding system and reproductive skew in a highly polygynous ant population

Abstract.: Factors affecting relatedness among nest members in ant colonies with high queen number are still poorly understood. In order to identify the major determinants of nest kin structure, we conducted a detailed analysis of the breeding system of the ant Formica exsecta. We estimated the number of mature queens by mark-release-recapture in 29 nests and dissected a sub-sample of queens to assess their reproductive status. We also used microsatellites to estimate relatedness within and between all classes of nestmates (queens, their mates, worker brood, queen brood and male brood). Queen number was very high, with an arithmetic mean of 253 per nest. Most queens (90%) were reproductively active, consistent with the genetic analyses revealing that there was only a minimal reproductive skew among nestmate queens. Despite the high queen number and low reproductive skew, almost all classes of individuals were significantly related to each other. Interestingly, the number of resident queens was a poor predictor of kin structure at the nest level, consistent with the observation that new queens are produced in bursts leading to highly fluctuating queen number across years. Queen number also varied tremendously across nests, with estimates ranging from five to several hundred queens. Accordingly, the harmonic mean queen number (40.5) was six times lower than the arithmetic mean. The variation in queen number was the most important factor of the breeding system contributing to a significant relatedness between almost all classes of nestmates despite a high average number of queens per nes

Measurement-induced localization of relative degrees of freedom

Published versio

Schwinger Algebra for Quaternionic Quantum Mechanics

It is shown that the measurement algebra of Schwinger, a characterization of the properties of Pauli measurements of the first and second kinds, forming the foundation of his formulation of quantum mechanics over the complex field, has a quaternionic generalization. In this quaternionic measurement algebra some of the notions of quaternionic quantum mechanics are clarified. The conditions imposed on the form of the corresponding quantum field theory are studied, and the quantum fields are constructed. It is shown that the resulting quantum fields coincide with the fermion or boson annihilation-creation operators obtained by Razon and Horwitz in the limit in which the number of particles in physical states $N \to \infty$.Comment: 20 pages, Plain Te

The embedding structure and the shift operator of the U(1) lattice current algebra

The structure of block-spin embeddings of the U(1) lattice current algebra is described. For an odd number of lattice sites, the inner realizations of the shift automorphism areclassified. We present a particular inner shift operator which admits a factorization involving quantum dilogarithms analogous to the results of Faddeev and Volkov.Comment: 14 pages, Plain TeX; typos and a terminological mishap corrected; version to appear in Lett.Math.Phy